Prediction of the flash point of ternary ideal mixtures
|
|
- Steven Parker
- 5 years ago
- Views:
Transcription
1 Electronc Journal of New Materals, Energy and Envronment Volume No. (25), -5 url: eissn: redcton of the flash pont of ternary deal mxtures M. Hrstova Unversty of Chemcal Technology and Metallurgy, 8 Kl. Ohrdsk Blvd., 756, Sofa, Bulgara E-mal: marana_hrstova@abv.bg Abstract The flash ponts of three organc ternary mxtures were measured n the present work. The expermental data was obtaned usng the ensky-martens closed cup tester. The expermental data were compared wth the values calculated by the Law s model by the applcaton of Raoult s law. The predcton results can be appled for nherently safer desgn for chemcal processes. Keywords: flash pont, ternary deal mxture, predcton, ensky-martens closed cup tester. Introducton One of the most mportant physcochemcal propertes for establshng the potental for fre and exploson of a hazardous substances and mxtures s ts flash pont (F). The F s related to the vapor pressure of a flammable lqud and s defned as the lowest temperature at whch t can form a combustble mxture wth ar []. Knowledge of the flash ponts s mportant for classfcaton of materals accordng to the classes defned n each partcular regulaton [2,3] and has great practcal sgnfcance n handlng, transport, storage and packagng of these materals. Flash ponts are determned expermentally by heatng the lqud n a contaner and then ntroducng a small flame just above the lqud surface. The temperature at whch there s a flash/gnton s recorded as the flash pont. Two general methods are called closed-cup and open-cup [4,5]. The closed-cup method prevents vapors from escapng and therefore usually results n a flash pont that s a few degrees lower than n an open cup. Because the two methods gve dfferent results, one must always lst the testng method when lstng the flash pont. Flash ponts of common pure chemcal substances are wdely reported, but very lmted data are avalable for mxtures. Ths fact may explan the decson of the EC (European communty) CL (Classfcaton, Labelng, and ackagng) [3] to delay the classfcaton of mxtures untl 25. Snce the expermental measurement of flash pont s expensve and tme consumng, predctve theoretcal methods are requred to estmate the flash ponts of both pure components and mxtures. Several predcton models are presented n the lterature for the predcton of mxture flash pont [6-]. Law et al. [2-6] have reported a seres of models, whch could be used for predctng the flash ponts for deal and non deal solutons. The basc assumpton n these models s that the lqud phase s n equlbrum wth the vapor. The purpose of ths study was to measure and predct the flash pont of ternary deal mxtures. The flash ponts were measured by ensky-martens closed cup tester, and compared wth the values calculated by usng Law s model and Raoult s law. RECEIVED: MARCH 5.25 AVAILABLE ONLINE: MARCH 5.25 COYRIGHT 25, ACADEMIA SERDICA ACTA LTD.
2 M. Hrstova / EJNMEE Experment The expermental data was obtaned usng the ensky-martens closed cup tester. The closed cup tester was operated accordng to the standard test method, EN ISO 279 [7]. The ambent barometrc pressure was observed and recorded at the tme of the test. When the pressure dffered from 76 mm Hg (.3 ka), the flash pont was corrected as follows: Corrected flash pont = T +.25(.3 ) where T s the observed flash pont (ºC); s barometrc pressure (ka). The mole fracton of each component was determned by measurng the mass usng a Sartorus dgtal balance (senstvty. g, maxmum load g). The sample was not strred whle the flame was lowered nto the cup. The flash pont was the temperature at whch the test flame applcaton caused a dstnct flash n the nteror of the cup. The measured value was the mean of two measurements whch do not dffer by more than 2ºC. 3. Mathematcal model for predctng the flash ponts of mscble deal mxtures Le Chateler s rule [8] for a flammable mxture of vapor + ar can be expressed as y LFL where y s the vapor phase composton of a flammable substance and LFL s the lower flammable lmt of the pure component. The LFL s expressed n relaton to the pure component vapor pressure at ts F,, as LFL, F (), (2) where s the ambent pressure. The flash pont of a substance s generally measured under atmosphere pressure. Under ths condton the vapor phase usually exhbts an deal behavor. In the case of a lqud mxture contanng flammable substances, the vapor lqud equlbrum of component s gven by where γ s the lqud phase actvty coeffcent. Substtutng Eqs. (2) and (3) nto Eq. () [9]: y x (3) x, (4) The vapor pressure for a pure substance s a functon of temperature and can be estmated by the Antone equaton: B log A (5) T C, The vapor pressure of pure lqud at ts flash pont, as presented n Eq. (4), can be estmated by substtutng T,, the flash pont of component, nto the Antone equaton. For an deal lqud mxture the actvty coeffcents of all components are equal to one, so Eq. (4) can be reduced to a smpler form, x, (6) For a ternary lqud soluton, Eq. (6) reduces to x, x 2 2 2, x 3 3 3, (7) - -
3 M. Hrstova / EJNMEE 25 Therefore, the reduced model for the flash pont-predcton under an deal soluton assumpton can be descrbed usng Eqs. (5) and (7). Table. Flash ponts and Antone coeffcents for pure components Substance CAS Flash pont [ C] Antone coeffcents* A B C * Heptane , ,37 26,636 Octane , ,82 26,385 Nonane , ,46 2,82 Dodecane , ,27 8,835 Benzene , ,76 29,6 Toluene , ,3 29,87 p-xylene , ,43 25,3 log ( ) B mmhg A T ( C ) C Three groups of ternary mxtures were selected to determne the expermental flash pont values. Accordng to the mathematcal model, the flash pont can also be obtaned usng calculatons. The measured flash ponts of studed ternary mxtures and the predcted by Law s model are presented n tables 2-4 respectvely, where T T T. exp ermental predcted Fgures -3 dsplay the predctve curves smulated by the model under an deal soluton assumpton. Table 2. Expermental flash ponts and predctons for heptane () + nonane (2) + dodecane (3) mxture X X 2 X 3 Exp. ( C) redct. ( C) C T,,,8 66, 64,5,5,,4,5 49,5 48,9,6,,6,3 4,5 39,6,9,2,5,3 34,5 35,5,,2,7, 26, 27,2,,5,2,3 25, 23,5,5,5,4, 5,5 6,,5,6,,3 2,5 9,6,9,7,,2,8 2,3,5,7,2, 9,5 8,9,6-2 -
4 M. Hrstova / EJNMEE 25 Mxture Contour lot of Fp (component amounts) Heptane Fp < > 8 Nonane Dodecane Fg.. Flash pont predcton results for mxture of heptane + nonane + dodecane Table 3. Expermental flash ponts and predctons for octane () + nonane (2) + dodecane (3) mxture X X 2 X 3 Exp. ( C) redct. ( C) C T,,2,7 6,5 6,7,2,,4,5 52,8 5,4,4,,5,4 48, 46,6,4,,8, 34, 33,3,7,2,2,6 56,5 54,5 2,,2,5,3 42,5 4,2 2,3,2,7, 3,5 3,6,,4,,5 46, 45,7,3,4,4,2 34,5 32,3,2,5,3,2 32,5 3,6,9 Mxture Contour lot of Fp (component amounts) Octane Fp < > 8 Nonane Dodecane Fg.2. Flash pont predcton results for mxture of octane + nonane + dodecane - 3 -
5 M. Hrstova / EJNMEE 25 Table 4. Expermental flash ponts and predctons for benzene () + toluene (2) + p-xylene (3) mxture X X 2 X 3 Exp. ( C) redct. ( C) C T,,2,8 2,5 9, 2,4,,5,75 9,8 8,2,6,,2,7 6,9 7,2,3,,5,4 3,,5,5,5,,75 8,5 7,2,3,2,,7 7, 5,4,6,2,3,5 3,,6,4,3,,6 3,5,7,8,3,3,4 9,5 7,9,6,35,,55, 9,8,2 Mxture Contour lot of Fp (component amounts) Benzene Fp < > 2 Toluene Xylene Fg.3. Flash pont predcton results for mxture of benzene + toluene + p-xylene The maxmum absolute devaton between the model and the expermental results s 2,4 C. The average absolute devaton s, C for heptane + nonane + dodecane mxture,,35 C for the octane+nonane+dodecane, and,47 C for benzene+toluene+p-xylene mxture. The model calculaton results are n a good agreement wth the expermental results, and, therefore, the model has good predctablty and applcablty. In the predcton model, t was assumed that the vapour phase and lqud phase of a soluton are n equlbrum. The predcted data was only adequate for the data determned by the closed cup test method, and may not be approprate to apply to the data obtaned from the open cup test method because of ts condton of havng devated from the vapour-lqud equlbrum. 5. Concluson The flash ponts of three ternary mxtures were measured by ensky-martens closed cup tester. The expermental data were compared wth values calculated by usng Law`s reduced model for the predcton of a soluton s flash-pont value for an assumed deal soluton. The model descrbed n ths paper s able accurately to predct the flash pont of a ternary deal solutons as revealed by a comparson between predcted and expermentally-derved data. The predcton results of ths model can be appled for nherently safer desgn for chemcal processes, such as the determnaton of the safe storage condtons for flammable solutons
6 M. Hrstova / EJNMEE 25 Estmaton of ternary mxture flash pont s very useful for the assessment of flammablty hazards, because t saves tme and effort. References [] Crowl D.A, Louvar J.F. Chemcal rocess Safety: fundamentals wth applcatons. 2nd ed. Upper Saddle Rver: rentce Hall TR; 22 [2] Regulaton (EC) No 97/26 of the European arlament and of the Councl concernng the Regstraton, Evaluaton, Authorzaton and Restrcton of Chemcals (REACH) [3] Regulaton (EC) No 97/26 of the European arlament and of the Councl concernng the Regstraton, Evaluaton, Authorzaton and Restrcton of Chemcals (REACH) [4] Amercan Socety for Testng and Materals, ASTM E 52-84: Selecton and Use of ASTM Standards for the Determnaton of Flash ont of Chemcals by Closed Cup Methods (ASTM Internatonal, West Conshohocken, A, 2) [5] Amercan Socety for Testng and Materals, ASTM 3: Standard Test Method for Flash ont and Fre ont of Lquds by Tag Open-Cup Apparatus (ASTM Internatonal, West Conshohocken, A, 2) [6] R.O. Wckey, D.H. Chttenden, Hydrocarb. rocess, 963, 42(6), [7] L. Catore, V. Naudet, J.hys.Chem.Ref.Data, 24, 33, 4, 83-, [8] L. Catore, S. aulmer, J. hys. Chem.Ref. Data, 26, 35,, 9-4 [9] J.L. McGovern, J. Coats Technol., 992, 64, 8, [] W.A. Affens, G.W. McLaren, J. Chem. Eng. Data, 972, 7, [] D. Whte, C.L. Beyler, C. Fulper, J. Leonard, Fre Saf. J., 997,28, -3 [2] H.-J. Law, Y.H. Lee, C.L. Tang, H.H. Hsu, J.H. Lu, J. Loss rev. rocess Ind., 22, 5, [3] H.-J. Law, Y.Y. Chu, J. Hazard. Mater., 23,, 83-6 [4] H.-J. Law, Y.Y. Chu, J. Hazard. Mater., 26, 37, [5] H.-J. Law, Y.H. Lee, Chen-Tsun, V.Gerbaud, Chem. Eng. Sc., 28, 63, [6] H.-J. Law, Y.H. Lee, V. Gerbaud, Y.H. L, Flud hase Equlb., 2, 3, 7-82 [7] EN ISO 279. Standard Test Methods for Flash ont by ensky-martens Closed Cup Tester [8] Le Chateler, H., Ann.Mnes, 9, 89, , [9] Law H-J, Tang C-L, La J-S.,Combust Flame 24,38,
Measurement and prediction of binary mixture flash point
Cent. Eur. J. Chem. 11(1) 2013 57-62 DOI: 10.2478/s11532-012-0131-1 Central European Journal of Chemstry Measurement and predcton of bnary mxture flash pont Research Artcle Marana Hrstova * Department
More informationFlash point of organic binary mixtures containing alcohols: experiment and prediction
Cent. Eur. J. Chem. 11(3) 2013 388-393 DOI: 10.2478/s11532-012-0171-6 Central European Journal of Chemistry Flash point of organic binary mixtures containing alcohols: experiment and prediction Research
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationIf two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.
9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson
More informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationI wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State
I wsh to publsh my paper on The Internatonal Journal of Thermophyscs. Ttle: A Practcal Method to Calculate Partal Propertes from Equaton of State Authors: Ryo Akasaka (correspondng author) 1 and Takehro
More informationEstimation of the composition of the liquid and vapor streams exiting a flash unit with a supercritical component
Department of Energ oltecnco d Mlano Va Lambruschn - 05 MILANO Eercses of Fundamentals of Chemcal rocesses rof. Ganpero Gropp Eercse 8 Estmaton of the composton of the lqud and vapor streams etng a unt
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationINTRODUCTION TO CHEMICAL PROCESS SIMULATORS
INTRODUCTION TO CHEMICAL PROCESS SIMULATORS DWSIM Chemcal Process Smulator A. Carrero, N. Qurante, J. Javaloyes October 2016 Introducton to Chemcal Process Smulators Contents Monday, October 3 rd 2016
More informationAssignment 4. Adsorption Isotherms
Insttute of Process Engneerng Assgnment 4. Adsorpton Isotherms Part A: Compettve adsorpton of methane and ethane In large scale adsorpton processes, more than one compound from a mxture of gases get adsorbed,
More informationGeneral Thermodynamics for Process Simulation. Dr. Jungho Cho, Professor Department of Chemical Engineering Dong Yang University
General Thermodynamcs for Process Smulaton Dr. Jungho Cho, Professor Department of Chemcal Engneerng Dong Yang Unversty Four Crtera for Equlbra μ = μ v Stuaton α T = T β α β P = P l μ = μ l1 l 2 Thermal
More informationGasometric Determination of NaHCO 3 in a Mixture
60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)
More informationEnergy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model
Lecture 4. Thermodynamcs [Ch. 2] Energy, Entropy, and Avalablty Balances Phase Equlbra - Fugactes and actvty coeffcents -K-values Nondeal Thermodynamc Property Models - P-v-T equaton-of-state models -
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationEVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES
EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge
More informationPETE 310 Lectures # 24 & 25 Chapter 12 Gas Liquid Equilibrium
ETE 30 Lectures # 24 & 25 Chapter 2 Gas Lqud Equlbrum Thermal Equlbrum Object A hgh T, Object B low T Intal contact tme Intermedate tme. Later tme Mechancal Equlbrum ressure essels Vale Closed Vale Open
More informationDetermination of Structure and Formation Conditions of Gas Hydrate by Using TPD Method and Flash Calculations
nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Determnaton of Structure and Formaton Condtons of Gas Hydrate by Usng TPD Method and Flash Calculatons H. Behat Rad, F. Varamnan* Department
More informationUniversity of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014
Lecture 16 8/4/14 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 214. Real Vapors and Fugacty Henry s Law accounts or the propertes o extremely dlute soluton. s shown n Fgure
More informationColor Rendering Uncertainty
Australan Journal of Basc and Appled Scences 4(10): 4601-4608 010 ISSN 1991-8178 Color Renderng Uncertanty 1 A.el Bally M.M. El-Ganany 3 A. Al-amel 1 Physcs Department Photometry department- NIS Abstract:
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationy i x P vap 10 A T SOLUTION TO HOMEWORK #7 #Problem
SOLUTION TO HOMEWORK #7 #roblem 1 10.1-1 a. In order to solve ths problem, we need to know what happens at the bubble pont; at ths pont, the frst bubble s formed, so we can assume that all of the number
More informationThe Measurement and Prediction of Flash Point for Binary Mixtures {C1 ~ C3 Alcohols + p-xylene} at kpa
Open Journal of Safety Scence and Technology, 2017, 7, 110 http://www.scrp.org/ournal/osst ISSN Onlne: 21626006 ISSN Prnt: 21625999 The Measurement and Predcton of Flash Pont for Bnary Mxtures {C1 ~ C3
More informationEquation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process
Equaton of State Modelng of Phase Equlbrum n the Low-Densty Polyethylene Process H. Orbey, C. P. Boks, and C. C. Chen Ind. Eng. Chem. Res. 1998, 37, 4481-4491 Yong Soo Km Thermodynamcs & Propertes Lab.
More informationBOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS. M. Krishna Reddy, B. Naveen Kumar and Y. Ramu
BOOTSTRAP METHOD FOR TESTING OF EQUALITY OF SEVERAL MEANS M. Krshna Reddy, B. Naveen Kumar and Y. Ramu Department of Statstcs, Osmana Unversty, Hyderabad -500 007, Inda. nanbyrozu@gmal.com, ramu0@gmal.com
More informationUNIFAC. Documentation. DDBSP Dortmund Data Bank Software Package
UNIFAC Documentaton DDBSP Dortmund Data Ban Software Pacage DDBST Dortmund Data Ban Software & Separaton Technology GmbH Mare-Cure-Straße 10 D-26129 Oldenburg Tel.: +49 441 361819 0 Fax: +49 441 361819
More informationCHEMICAL ENGINEERING
Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton
More information3. Be able to derive the chemical equilibrium constants from statistical mechanics.
Lecture #17 1 Lecture 17 Objectves: 1. Notaton of chemcal reactons 2. General equlbrum 3. Be able to derve the chemcal equlbrum constants from statstcal mechancs. 4. Identfy how nondeal behavor can be
More information( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.
Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.
More informationMass Transfer Processes
Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.
More informationAdiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram
Adabatc Sorpton of Ammona-Water System and Depctng n p-t-x Dagram J. POSPISIL, Z. SKALA Faculty of Mechancal Engneerng Brno Unversty of Technology Techncka 2, Brno 61669 CZECH REPUBLIC Abstract: - Absorpton
More informationAppendix II Summary of Important Equations
W. M. Whte Geochemstry Equatons of State: Ideal GasLaw: Coeffcent of Thermal Expanson: Compressblty: Van der Waals Equaton: The Laws of Thermdynamcs: Frst Law: Appendx II Summary of Important Equatons
More informationExercises of Fundamentals of Chemical Processes
Department of Energ Poltecnco d Mlano a Lambruschn 4 2056 MILANO Exercses of undamentals of Chemcal Processes Prof. Ganpero Gropp Exercse 7 ) Estmaton of the composton of the streams at the ext of an sothermal
More informationA Self-Consistent Gibbs Excess Mixing Rule for Cubic Equations of State: derivation and fugacity coefficients
A Self-Consstent Gbbs Excess Mxng Rule for Cubc Equatons of State: dervaton and fugacty coeffcents Paula B. Staudt, Rafael de P. Soares Departamento de Engenhara Químca, Escola de Engenhara, Unversdade
More informationPrediction of Ultrasonic Velocity in Binary Mixtures of a Nuclear Extractant and Monocarboxylic Acids using Several Theoretical Models
Predcton of ltrasonc Velocty n Bnary Mxtures of a Nuclear Extractant and Monocarboxylc Acds usng Several Theoretcal Models R. K. Mshra 1, B. Dala 1*, N. Swan 2 and S.K. Dash 3 1 BSH, Gandh Insttute of
More information10.34 Numerical Methods Applied to Chemical Engineering Fall Homework #3: Systems of Nonlinear Equations and Optimization
10.34 Numercal Methods Appled to Chemcal Engneerng Fall 2015 Homework #3: Systems of Nonlnear Equatons and Optmzaton Problem 1 (30 ponts). A (homogeneous) azeotrope s a composton of a multcomponent mxture
More informationPrediction of steady state input multiplicities for the reactive flash separation using reactioninvariant composition variables
Insttuto Tecnologco de Aguascalentes From the SelectedWorks of Adran Bonlla-Petrcolet 2 Predcton of steady state nput multplctes for the reactve flash separaton usng reactonnvarant composton varables Jose
More informationVapor-Liquid Equilibria for Water+Hydrochloric Acid+Magnesium Chloride and Water+Hydrochloric Acid+Calcium Chloride Systems at Atmospheric Pressure
Chnese J. Chem. Eng., 4() 76 80 (006) RESEARCH OES Vapor-Lqud Equlbra for Water+Hydrochlorc Acd+Magnesum Chlorde and Water+Hydrochlorc Acd+Calcum Chlorde Systems at Atmospherc Pressure ZHAG Yng( 张颖 ) and
More information2016 Wiley. Study Session 2: Ethical and Professional Standards Application
6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton
More informationSimulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests
Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth
More informationChapter 13: Multiple Regression
Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to
More informationRegularized Discriminant Analysis for Face Recognition
1 Regularzed Dscrmnant Analyss for Face Recognton Itz Pma, Mayer Aladem Department of Electrcal and Computer Engneerng, Ben-Guron Unversty of the Negev P.O.Box 653, Beer-Sheva, 845, Israel. Abstract Ths
More informationLab 2e Thermal System Response and Effective Heat Transfer Coefficient
58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),
More informationChapter 9: Statistical Inference and the Relationship between Two Variables
Chapter 9: Statstcal Inference and the Relatonshp between Two Varables Key Words The Regresson Model The Sample Regresson Equaton The Pearson Correlaton Coeffcent Learnng Outcomes After studyng ths chapter,
More informationMODELING THE HIGH-PRESSURE BEHAVIOR OF BINARY MIXTURES OF CARBON DIOXIDE+ALKANOLS USING AN EXCESS FREE ENERGY MIXING RULE
Brazlan Journal of Chemcal Engneerng ISSN 0104-6632 Prnted n Brazl Vol. 21, No. 04, pp. 659-666, October - December 04 MODELING THE HIGH-PRESSURE BEHAVIOR OF BINARY MIXTURES OF CARBON DIOXIDE+ALKANOLS
More informationDepartment of Physical Chemistry, Faculty of Chemistry, University of Bucharest, Bd. Regina Elisabeta 4-12, , Bucharest, Romania
ISOTHERMAL LIQUID-VAOR EQUILIBRIUM IN ACETONITRILE-WATER SYSTEM Rodca Vlcu, Zoca Cenuse abstact: The study of ths system started from the mportance that acetontrle has as the component of some mxtures
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationAdsorption: A gas or gases from a mixture of gases or a liquid (or liquids) from a mixture of liquids is bound physically to the surface of a solid.
Searatons n Chemcal Engneerng Searatons (gas from a mxture of gases, lquds from a mxture of lquds, solds from a soluton of solds n lquds, dssolved gases from lquds, solvents from gases artally/comletely
More informationPredictive Analytics : QM901.1x Prof U Dinesh Kumar, IIMB. All Rights Reserved, Indian Institute of Management Bangalore
Sesson Outlne Introducton to classfcaton problems and dscrete choce models. Introducton to Logstcs Regresson. Logstc functon and Logt functon. Maxmum Lkelhood Estmator (MLE) for estmaton of LR parameters.
More informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More informationGrand canonical Monte Carlo simulations of bulk electrolytes and calcium channels
Grand canoncal Monte Carlo smulatons of bulk electrolytes and calcum channels Thess of Ph.D. dssertaton Prepared by: Attla Malascs M.Sc. n Chemstry Supervsor: Dr. Dezső Boda Unversty of Pannona Insttute
More informationDetermination of activity coefficients of dimethyl ether in butyl acetate and 2-propanol
Determnaton of actvty coeffcents of dmethyl ether n butyl acetate and 2-propanol Petar Petrov Determnaton of actvty coeefcents of dmethyl ether n butyl acetate and 2-propanol: The paper presents expermental
More informationNAME and Section No. it is found that 0.6 mol of O
NAME and Secton No. Chemstry 391 Fall 7 Exam III KEY 1. (3 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). In the reacton 3O O3 t s found that.6 mol of O are consumed. Fnd
More informationComparison of Regression Lines
STATGRAPHICS Rev. 9/13/2013 Comparson of Regresson Lnes Summary... 1 Data Input... 3 Analyss Summary... 4 Plot of Ftted Model... 6 Condtonal Sums of Squares... 6 Analyss Optons... 7 Forecasts... 8 Confdence
More informationVAPOR LIQUID EQUILIBRIUM DATA GENERATION FOR ACETIC ACID AND p-xylene AT ATMOSPHERIC PRESSURE
Int. J. Chem. Sc.: 14(3), 2016, 1511-1519 ISSN 0972-768X www.sadgurupublcatons.com VAPOR LIQUID EQUILIBRIUM DATA GENERATION FOR ACETIC ACID AND p-xylene AT ATMOSPHERIC PRESSURE PAWAN KIRAN MALI *,a and
More informationDepartment of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution
Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationONE DIMENSIONAL TRIANGULAR FIN EXPERIMENT. Technical Advisor: Dr. D.C. Look, Jr. Version: 11/03/00
ONE IMENSIONAL TRIANGULAR FIN EXPERIMENT Techncal Advsor: r..c. Look, Jr. Verson: /3/ 7. GENERAL OJECTIVES a) To understand a one-dmensonal epermental appromaton. b) To understand the art of epermental
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationDETERMINATION OF CO 2 MINIMUM MISCIBILITY PRESSURE USING SOLUBILITY PARAMETER
DETERMINATION OF CO 2 MINIMUM MISCIBILITY PRESSURE USING SOLUBILITY PARAMETER Rocha, P. S. 1, Rbero, A. L. C. 2, Menezes, P. R. F. 2, Costa, P. U. O. 2, Rodrgues, E. A. 2, Costa, G. M. N. 2 *, glora.costa@unfacs.br,
More informationA novel mathematical model of formulation design of emulsion explosive
J. Iran. Chem. Res. 1 (008) 33-40 Journal of the Iranan Chemcal Research IAU-ARAK www.au-jcr.com A novel mathematcal model of formulaton desgn of emulson explosve Mng Lu *, Qfa Lu Chemcal Engneerng College,
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationSolution Thermodynamics
Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs
More informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationSTATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION
STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros
More informationThe Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More informationCOEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN
Int. J. Chem. Sc.: (4), 04, 645654 ISSN 097768X www.sadgurupublcatons.com COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN R. GOVINDARASU a, R. PARTHIBAN a and P. K. BHABA b* a Department
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationBe true to your work, your word, and your friend.
Chemstry 13 NT Be true to your work, your word, and your frend. Henry Davd Thoreau 1 Chem 13 NT Chemcal Equlbrum Module Usng the Equlbrum Constant Interpretng the Equlbrum Constant Predctng the Drecton
More informationName: SID: Discussion Session:
Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether
More informationME 300 Exam 2 November 18, :30 p.m. to 7:30 p.m.
CICLE YOU LECTUE BELOW: Frst Name Last Name 1:3 a.m. 1:3 p.m. Nak Gore ME 3 Exam November 18, 14 6:3 p.m. to 7:3 p.m. INSTUCTIONS 1. Ths s a closed book and closed notes examnaton. You are provded wth
More informationCalculus of Variations Basics
Chapter 1 Calculus of Varatons Bascs 1.1 Varaton of a General Functonal In ths chapter, we derve the general formula for the varaton of a functonal of the form J [y 1,y 2,,y n ] F x,y 1,y 2,,y n,y 1,y
More informationOFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES
ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty
More informationNumber Average Molar Mass. Mass Average Molar Mass. Z-Average Molar Mass
17 Molar mass: There are dfferent ways to report a molar mass lke (a) Number average molar mass, (b) mass average molar mass, (c) Vscosty average molar mass, (d) Z- Average molar mass Number Average Molar
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationLecture. Polymer Thermodynamics 0331 L Chemical Potential
Prof. Dr. rer. nat. habl. S. Enders Faculty III for Process Scence Insttute of Chemcal Engneerng Department of Thermodynamcs Lecture Polymer Thermodynamcs 033 L 337 3. Chemcal Potental Polymer Thermodynamcs
More informationPhase equilibria for the oxygen-water system up to elevated temperatures and pressures
Phase equlbra for the oxygen-water system up to elevated temperatures and pressures Xaoyan J 1, 2, Xaohua Lu 2, Jnyue Yan 1,3* 1 Department of Chemcal Engneerng and Technology / Energy Processes, Royal
More informationElectrochemical Equilibrium Electromotive Force
CHM465/865, 24-3, Lecture 5-7, 2 th Sep., 24 lectrochemcal qulbrum lectromotve Force Relaton between chemcal and electrc drvng forces lectrochemcal system at constant T and p: consder Gbbs free energy
More informationOver-Temperature protection for IGBT modules
Over-Temperature protecton for IGBT modules Ke Wang 1, Yongjun Lao 2, Gaosheng Song 1, Xanku Ma 1 1 Mtsubsh Electrc & Electroncs (Shangha) Co., Ltd., Chna Room2202, Tower 3, Kerry Plaza, No.1-1 Zhongxns
More informationPrediction and measurement of the lower flash points for flammable binary solutions by using a setaflash closed cup tester
Korean J. Chem. Eng., 8(5), 1161-1165 (011) DOI: 10.1007/s11814-010-0478-y INVITED REVIEW PAPER Prediction and measurement of the lower flash points for flammable binary solutions by using a setaflash
More informationModeling Interfacial Tension in Liquid Liquid Systems Containing Electrolytes
Artcle pubs.acs.org/iecr Modelng Interfacal Tenson n Lqud Lqud Systems Contanng Electrolytes Pemng Wang* and Andrzej Anderko OLI Systems Inc., 240 Cedar Knolls Road, Sute 3, Cedar Knolls, New Jersey 07927,
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More informationIrregular vibrations in multi-mass discrete-continuous systems torsionally deformed
(2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected
More informationNew Perturbation Model for Prediction of Amino Acid and Peptide Activity Coefficients
Iranan Journal of Chemcal Engneerng Vol. 9, No. 2 (Sprng), 2012, IAChE Resea rch note New Perturbaton Model for Predcton of Amno Acd and Peptde Actvty Coeffcents M. R. Dehghan 1, E. Saleh 1,2, A. R. Fazlal
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationBeyond Zudilin s Conjectured q-analog of Schmidt s problem
Beyond Zudln s Conectured q-analog of Schmdt s problem Thotsaporn Ae Thanatpanonda thotsaporn@gmalcom Mathematcs Subect Classfcaton: 11B65 33B99 Abstract Usng the methodology of (rgorous expermental mathematcs
More informationMACHINE APPLIED MACHINE LEARNING LEARNING. Gaussian Mixture Regression
11 MACHINE APPLIED MACHINE LEARNING LEARNING MACHINE LEARNING Gaussan Mture Regresson 22 MACHINE APPLIED MACHINE LEARNING LEARNING Bref summary of last week s lecture 33 MACHINE APPLIED MACHINE LEARNING
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationOn Tiling for Some Types of Manifolds. and their Folding
Appled Mathematcal Scences, Vol. 3, 009, no. 6, 75-84 On Tlng for Some Types of Manfolds and ther Foldng H. Rafat Mathematcs Department, Faculty of Scence Tanta Unversty, Tanta Egypt hshamrafat005@yahoo.com
More information(1) The saturation vapor pressure as a function of temperature, often given by the Antoine equation:
CE304, Sprng 2004 Lecture 22 Lecture 22: Topcs n Phase Equlbra, part : For the remander of the course, we wll return to the subject of vapor/lqud equlbrum and ntroduce other phase equlbrum calculatons
More informationDERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION
Internatonal Worshop ADVANCES IN STATISTICAL HYDROLOGY May 3-5, Taormna, Italy DERIVATION OF THE PROBABILITY PLOT CORRELATION COEFFICIENT TEST STATISTICS FOR THE GENERALIZED LOGISTIC DISTRIBUTION by Sooyoung
More informationProcess Modeling. Improving or understanding chemical process operation is a major objective for developing a dynamic process model
Process Modelng Improvng or understandng chemcal process operaton s a major objectve for developng a dynamc process model Balance equatons Steady-state balance equatons mass or energy mass or energy enterng
More informationCHAPTER 4 MAX-MIN AVERAGE COMPOSITION METHOD FOR DECISION MAKING USING INTUITIONISTIC FUZZY SETS
56 CHAPER 4 MAX-MIN AVERAGE COMPOSIION MEHOD FOR DECISION MAKING USING INUIIONISIC FUZZY SES 4.1 INRODUCION Intutonstc fuzz max-mn average composton method s proposed to construct the decson makng for
More informationStatistics for Economics & Business
Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable
More informationParameter Estimation for Dynamic System using Unscented Kalman filter
Parameter Estmaton for Dynamc System usng Unscented Kalman flter Jhoon Seung 1,a, Amr Atya F. 2,b, Alexander G.Parlos 3,c, and Klto Chong 1,4,d* 1 Dvson of Electroncs Engneerng, Chonbuk Natonal Unversty,
More information